Levy-Student Distributions for Halos in Accelerator Beams

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Shchr\"odinger--like (\Sl) equation. The space charge effects have been introduced in a recent paper~\cite{prstab} by coupling this \Sl equation with the Maxwell equations. We analyze the space charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self--consistent solutions are related to the (external, and space--charge) potentials both when we suppose that the external field is harmonic (\emph{constant focusing}), and when we \emph{a priori} prescribe the shape of the stationary solution. We then proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized Student distributions, namely non--Gaussian, L\'evy \emph{infinitely divisible} (but not \emph{stable}) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non--Gaussian) L\'evy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the L\'evy--Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.Comment: revtex4, 18 pages, 12 figure

Stochastic collective dynamics of charged--particle beams in the stability regime

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by $\lambda_c\sqrt{N}$, where $N$ is the number of particles in the beam and $\lambda_c$ the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schr\"odinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so--called ``quantum--like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam--field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.Comment: 15 pages, 9 figure

Mass spectrum from stochastic Levy-Schroedinger relativistic equations: possible qualitative predictions in QCD

Starting from the relation between the kinetic energy of a free Levy-Schroedinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cut-off in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model.Comment: 8 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1008.425

Handling of household and item nonresponse in surveys

Für den Zensus 2000 wird das US Census Bureau eine Stichprobe zur Qualitätsprüfung auswählen (auch bekannt als integrated coverage measurement oder ICM), die die Schätzungen des Zensus verbessern soll. Die ICM-Stichprobe wird durch fehlende Daten aufgrund von Antwortverweigerung der befragten Haushalte oder Antwortverweigerung auf einzelne Fragen beeinflusst. Der Verfasser diskutiert alternative Methoden zur Berücksichtigung von Antwortverweigerung in der ICM-Stichprobe. Hierzu zählen folgende Vorgehensweisen: (1) keine Korrektur bei Antwortverweigerung durch Haushalte und keine Ableitung von Items; (2) Korrektur bei Antwortverweigerung durch Haushalte auf der Basis der Zensus-Kurzcharakteristiken; (3) Ersatz fehlender ICM-Items durch Zensusdaten; (4) Hot-Deck-Ableitungsverfahren. (ICEÜbers)"For the 2000 Census, the U.S. Census Bureau will select a quality check, also known as integrated coverage measurement (ICM), sample to improve Census estimates. The ICM sample is subject to missing data due to household and item nonresponse. This paper discusses alternative methods researched to deal with nonresponse in the ICM sample. These methods include no adjustment for household nonresponse and no item imputation, use of Census short form characteristics to perform household nonresponse adjustment, substitution of Census data for ICM missing items, and alternative hot deck imputation procedures." (author's abstract

Weighted-indexed semi-Markov models for modeling financial returns

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010.Comment: arXiv admin note: substantial text overlap with arXiv:1109.425

Lexical evolution rates by automated stability measure

Phylogenetic trees can be reconstructed from the matrix which contains the distances between all pairs of languages in a family. Recently, we proposed a new method which uses normalized Levenshtein distances among words with same meaning and averages on all the items of a given list. Decisions about the number of items in the input lists for language comparison have been debated since the beginning of glottochronology. The point is that words associated to some of the meanings have a rapid lexical evolution. Therefore, a large vocabulary comparison is only apparently more accurate then a smaller one since many of the words do not carry any useful information. In principle, one should find the optimal length of the input lists studying the stability of the different items. In this paper we tackle the problem with an automated methodology only based on our normalized Levenshtein distance. With this approach, the program of an automated reconstruction of languages relationships is completed

Autophagy in major human diseases

Autophagy is a core molecular pathway for the preservation of cellular and organismal homeostasis. Pharmacological and genetic interventions impairing autophagy responses promote or aggravate disease in a plethora of experimental models. Consistently, mutations in autophagy-related processes cause severe human pathologies. Here, we review and discuss preclinical data linking autophagy dysfunction to the pathogenesis of major human disorders including cancer as well as cardiovascular, neurodegenerative, metabolic, pulmonary, renal, infectious, musculoskeletal, and ocular disorders

Quantum Mechanical Interaction-Free Measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.Comment: (revised file with no need for macro), 12, TAUP 1865-91

Classical Cepheid Pulsation Models: IX. New Input Physics

We constructed several sequences of classical Cepheid envelope models at solar chemical composition ($Y=0.28, Z=0.02$) to investigate the dependence of the pulsation properties predicted by linear and nonlinear hydrodynamical models on input physics. To study the dependence on the equation of state (EOS) we performed several numerical experiments by using the simplified analytical EOS originally developed by Stellingwerf and the recent analytical EOS developed by Irwin. Current findings suggest that the pulsation amplitudes as well as the topology of the instability strip marginally depend on the adopted EOS. We also investigated the dependence of observables predicted by theoretical models on the mass-luminosity (ML) relation and on the spatial resolution across the Hydrogen and the Helium partial ionization regions. We found that nonlinear models are marginally affected by these physical and numerical assumptions. In particular, the difference between new and old models in the location as well as in the temperature width of the instability strip is on average smaller than 200 K. However, the spatial resolution somehow affects the pulsation properties. The new fine models predict a period at the center of the Hertzsprung Progression ($P_{HP}=9.65$$-$9.84 days) that reasonably agree with empirical data based on light curves ($P_{HP}=10.0\pm 0.5$ days; \citealt{mbm92}) and on radial velocity curves ($P_{HP}=9.95\pm 0.05$ days; \citealt{mall00}), and improve previous predictions by Bono, Castellani, and Marconi (2000, hereinafter BCM00).Comment: 35 pages, 7 figures. Accepted for publication in the Astrophysical Journa

Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure